Cosmology School Lecture on Modified Gravity                            Lam Hui’s collaborators:                          ...
Topics for discussions:          - Scalar-tensor theory as a framework for modifying gravity            Weinberg’s theorem...
Scalar-tensor theories              Weinberg/Deser theorem tells us that a Lorentz invariant theory of a massless         ...
Topics for discussions:          - Scalar-tensor theory as a framework for modifying gravity            Weinberg’s theorem...
Scalar-tensor theories              Weinberg/Deser theorem tells us that a Lorentz invariant theory of a massless         ...
Topics for discussions:          - Scalar-tensor theory as a framework for modifying gravity            Weinberg’s theorem...
Topics for discussions:          - Scalar-tensor theory as a framework for modifying gravity            Weinberg’s theorem...
Scalar-tensor theories              Weinberg/Deser theorem tells us that a Lorentz invariant theory of a massless         ...
Topics for discussions:          - Scalar-tensor theory as a framework for modifying gravity            Weinberg’s theorem...
Khoury         Chameleon screening - environment dependent mass                                                Weltman    ...
Constrasting chameleon and Vainshtein screening:             Consider an object in the presence of a long wavelength exter...
Observational tests of chameleon screening          An object is chameleon screened (Q  M) if the -grav. potential        ...
Bulk motion tests:         Idea - unscreened small galaxies, screened large galaxies.         1. Small galaxies should mov...
Ruled out by demanding                                         screening in Milky way and sun                            α...
Side remark: chameleon theories cannot support genuine         self-acceleration.                                         ...
Observational test of the Vainshtein mechanism           It would be nice if there are equivalence principle tests of the ...
Observational test of the Vainshtein mechanism           It would be nice if there are equivalence principle tests of the ...
Observational test of the Vainshtein mechanism           It would be nice if there are equivalence principle tests of the ...
Observational test of the Vainshtein mechanism           It would be nice if there are equivalence principle tests of the ...
Observational test of the Vainshtein mechanism           It would be nice if there are equivalence principle tests of the ...
Chan  Scoccimarro 2009                                                                     9 FIG. 5: Dark matter power spe...
The key is to recognize that there are regions in the universe           where the scalar ϕ is in the linear regime - in a...
The key is to recognize that there are regions in the universe           where the scalar ϕ is in the linear regime - in a...
The idea is to look for the offset of massive black holes from the            centers of galaxies which are streaming out ...
Topics for discussions:          - Scalar-tensor theory as a framework for modifying gravity            Weinberg’s theorem...
Upcoming SlideShare
Loading in …5
×

Hui - modified gravity

3,071 views

Published on

Published in: Technology
0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total views
3,071
On SlideShare
0
From Embeds
0
Number of Embeds
678
Actions
Shares
0
Downloads
51
Comments
0
Likes
0
Embeds 0
No embeds

No notes for slide

Hui - modified gravity

  1. 1. Cosmology School Lecture on Modified Gravity Lam Hui’s collaborators: Chameleon screening - Alberto Nicolis, Chris Stubbs - Phil Chang - Justin Khoury, Junpu Wang Vainshtein screening - Alberto NicolisTuesday, January 24, 2012
  2. 2. Topics for discussions: - Scalar-tensor theory as a framework for modifying gravity Weinberg’s theorem, quintessence - Conformal transformation: Einstein vs Jordan frame - Connection with self-acceleration - Large scale tests - Small scale testsTuesday, January 24, 2012
  3. 3. Scalar-tensor theories Weinberg/Deser theorem tells us that a Lorentz invariant theory of a massless spin 2 particle must be GR at low energies. Thus modified gravity often introduce new d.o.f. such as scalars (e.g. DGP, f(R), massive graviton, degravitation, TeVeS, healthy extensions of Horava gravity ...) Absent symmetries, quintessence should be coupled to matter. Let’s consider (Einstein frame): 1 S= d x − (∂ϕ)2 + Lint (ϕ) + αϕTm + ... + hµν Tm µν 4 2 gµν = ηµν + hµν ϕ dimensionless, MP = 1 α = scalar-matter coupling = O(1) ϕ mediates a long range force, which must be screened to satisfy solar system tests. Lint (ϕ) determines the screening mechanism - potential interactions give chameleon, derivative interactions give Vainshtein.Tuesday, January 24, 2012
  4. 4. Topics for discussions: - Scalar-tensor theory as a framework for modifying gravity Weinberg’s theorem, quintessence - Conformal transformation: Einstein vs Jordan frame Einstein: extra (5th) force; Jordan: geodesic for test particle (only!) - Connection with self-acceleration - Large scale tests - Small scale testsTuesday, January 24, 2012
  5. 5. Scalar-tensor theories Weinberg/Deser theorem tells us that a Lorentz invariant theory of a massless spin 2 particle must be GR at low energies. Thus modified gravity often introduce new d.o.f. such as scalars (e.g. DGP, f(R), massive graviton, degravitation, TeVeS, healthy extensions of Horava gravity ...) Absent symmetries, quintessence should be coupled to matter. Let’s consider (Einstein frame): 1 S= d x − (∂ϕ)2 + Lint (ϕ) + αϕTm + ... + hµν Tm µν 4 2 gµν = ηµν + hµν ϕ dimensionless, MP = 1 α = scalar-matter coupling = O(1) ϕ mediates a long range force, which must be screened to satisfy solar system tests. Lint (ϕ) determines the screening mechanism - potential interactions give chameleon, derivative interactions give Vainshtein.Tuesday, January 24, 2012
  6. 6. Topics for discussions: - Scalar-tensor theory as a framework for modifying gravity Weinberg’s theorem, quintessence - Conformal transformation: Einstein vs Jordan frame Einstein: extra (5th) force; Jordan: geodesic for test particle (only!) - Connection with self-acceleration Self-acceleration versus acceleration by dark energy - Large scale tests - Small scale testsTuesday, January 24, 2012
  7. 7. Topics for discussions: - Scalar-tensor theory as a framework for modifying gravity Weinberg’s theorem, quintessence - Conformal transformation: Einstein vs Jordan frame Einstein: extra (5th) force; Jordan: geodesic for test particle (only!) - Connection with self-acceleration Self-acceleration versus acceleration by dark energy - Large scale tests Growth rate, Psi versus Phi, photons - Small scale testsTuesday, January 24, 2012
  8. 8. Scalar-tensor theories Weinberg/Deser theorem tells us that a Lorentz invariant theory of a massless spin 2 particle must be GR at low energies. Thus modified gravity often introduce new d.o.f. such as scalars (e.g. DGP, f(R), massive graviton, degravitation, TeVeS, healthy extensions of Horava gravity ...) Absent symmetries, quintessence should be coupled to matter. Let’s consider (Einstein frame): 1 S= d x − (∂ϕ)2 + Lint (ϕ) + αϕTm + ... + hµν Tm µν 4 2 gµν = ηµν + hµν ϕ dimensionless, MP = 1 α = scalar-matter coupling = O(1) ϕ mediates a long range force, which must be screened to satisfy solar system tests. Lint (ϕ) determines the screening mechanism - potential interactions give chameleon, derivative interactions give Vainshtein.Tuesday, January 24, 2012
  9. 9. Topics for discussions: - Scalar-tensor theory as a framework for modifying gravity Weinberg’s theorem, quintessence - Conformal transformation: Einstein vs Jordan frame Einstein: extra (5th) force; Jordan: geodesic for test particle (only!) - Connection with self-acceleration Self-acceleration versus acceleration by dark energy - Large scale tests Growth rate, Psi versus Phi, photons - Small scale tests Screening mechanisms: chameleon versus Vainshtein Violations of the equivalence principle: chameleon - non-relativistic; Vainshtein - relativistic.Tuesday, January 24, 2012
  10. 10. Khoury Chameleon screening - environment dependent mass Weltman 1 Sscalar ∼ d x − (∂ϕ)2 − V (ϕ) + αϕTm µ µ 4 (Einstein frame) 2 e.o.m.: V (ϕ) αρm ϕ ✷ϕ ∼ [V + αρm ϕ],ϕ (Tm µ µ ∼ −ρm ) (ϕ dimensionless, MP = 1 ) ϕ See also: symmetron(Hinterbichler, Khoury) Vainshtein screening - scale dependent interactions e.g. DGP 1 1 (Einstein frame) Sscalar ∼ 4 2 d x − (∂ϕ) − 2 (∂ϕ)2 ✷ϕ + αϕTm µ µ 2 m 1 ϕ∝ large r e.o.m.: ✷ϕ + 1 (✷ϕ)2 − ∂ µ∂ ν ϕ∂µ ∂ν ϕ ∼ αρm r 2 m √ ϕ ∝ r small r ϕ graviton mass √ point mass solution r r−1 See also: galileon (Nicolis, Rattazzi, Trincherini) r rV ∼ (rSchw m−2 )1/3 α = scalar-matter coupling = O(1) genericallyTuesday, January 24, 2012
  11. 11. Constrasting chameleon and Vainshtein screening: Consider an object in the presence of a long wavelength external ϕ (i.e. ignoring tides). The object-scalar interaction is described by Sint ∼ −αQ dτ ϕ where Q is the object’s scalar charge i.e. F = −αQ∇ϕ . Chameleon: e.g. both have Q M , because ∇2 ϕ = V,ϕ + αρm ∼ 0 earth sun Vainshtein: e.g. both have Q = M , because shift symmetry implies e.o.m. takes the Gauss-law rV form ∂ · J = αρm A large scalar force on the earth is avoided by having the sun source a very suppressed scalar profile within the Vainshtein radius.Tuesday, January 24, 2012
  12. 12. Observational tests of chameleon screening An object is chameleon screened (Q M) if the -grav. potential (GM/R) is deeper than ϕext /α , and unscreened (Q=M) otherwise. Observationally, we know any object with -grav. pot. deeper than 10−6 should be screened (from Milky way). A screened object does not experience scalar force, while an unscreened object does. They therefore fall at rates that are O(1) different (violation of equivalence principle) i.e. object dependent G. Note: a screened object does not move on Jordan frame geodesic! Red giants would have a compact screened core, and a diffuse unscreened envelope. Thus, effectively Newton’s G changes value in the star. This affects the observed temperature at the 100 K level.Tuesday, January 24, 2012
  13. 13. Bulk motion tests: Idea - unscreened small galaxies, screened large galaxies. 1. Small galaxies should move faster than large galaxies (i.e. an effective velocity bias - redshift distortion needs to be reworked) in unscreened environments. Beware: Yukawa suppression. 2. Small galaxies should stream out of voids faster than large galaxies creating larger than expected voids defined by small galaxies (see Peebles; note: effect cares about sign of grav. pot.). Internal motion tests: Idea - unscreened HI gas clouds, screened stars. 3. Diffuse gas (e.g. HI) should move faster than stars in small galaxies even if they are on the same orbit. Beware: asymmetric drift. 4. Gravitational lensing mass should agree with dynamical mass from stars, but disagree with that from HI in small galaxies. Key: avoid blanket screening.Tuesday, January 24, 2012
  14. 14. Ruled out by demanding screening in Milky way and sun αscalar-matter coupling 1/ 6 10 −8 10 −6 ϕ = scalar field value at mean density ϕ/αTuesday, January 24, 2012
  15. 15. Side remark: chameleon theories cannot support genuine self-acceleration. gµν = eαϕ gµν ˜ Jordan frame metric Einstein frame metric Want no acceleration in Einstein frame, but acceleration in Jordan frame i.e. do not want acceleration to be caused by some form of dark energy, but rather by the non-minimal scalar coupling itself. This suggests αϕ cannot be too small. Since observations constrain ϕ/α 10−6 for chameleon ∼ screening, it cannot support self-acceleration whatever the actual model is (assuming α ∼ 1).Tuesday, January 24, 2012
  16. 16. Observational test of the Vainshtein mechanism It would be nice if there are equivalence principle tests of the sort like those for chameleon.Tuesday, January 24, 2012
  17. 17. Observational test of the Vainshtein mechanism It would be nice if there are equivalence principle tests of the sort like those for chameleon. But we know already Q=M is respected by derivative interactions. Thus different objects fall at the same rate (i.e. “grav. charge/mass” = inertial mass).Tuesday, January 24, 2012
  18. 18. Observational test of the Vainshtein mechanism It would be nice if there are equivalence principle tests of the sort like those for chameleon. But we know already Q=M is respected by derivative interactions. Thus different objects fall at the same rate (i.e. “grav. charge/mass” = inertial mass). Wait! How about black holes, they have zero scalar charge right? Won’t they fall slower than stars? i.e. equivalence principle violation of the relativistic kind.Tuesday, January 24, 2012
  19. 19. Observational test of the Vainshtein mechanism It would be nice if there are equivalence principle tests of the sort like those for chameleon. But we know already Q=M is respected by derivative interactions. Thus different objects fall at the same rate (i.e. “grav. charge/mass” = inertial mass). Wait! How about black holes, they have zero scalar charge right? Won’t they fall slower than stars? i.e. equivalence principle violation of the relativistic kind. Issue 1: the existing derivations of no-scalar-hair theorem do not apply to galileons, but we can extend them to show black holes have no galileon hair (at the moment for Schwarzchild).Tuesday, January 24, 2012
  20. 20. Observational test of the Vainshtein mechanism It would be nice if there are equivalence principle tests of the sort like those for chameleon. But we know already Q=M is respected by derivative interactions. Thus different objects fall at the same rate (i.e. “grav. charge/mass” = inertial mass). Wait! How about black holes, they have zero scalar charge right? Won’t they fall slower than stars? i.e. equivalence principle violation of the relativistic kind. Issue 1: the existing derivations of no-scalar-hair theorem do not apply to galileons, but we can extend them to show black holes have no galileon hair (at the moment for Schwarzchild). Issue 2, a more serious problem: black holes and stars are generally found inside galaxies. Wouldn’t the fact that they are both inside the Vainshtein radius of the galaxy mean the effect is very small?Tuesday, January 24, 2012
  21. 21. Chan Scoccimarro 2009 9 FIG. 5: Dark matter power spectra from the nonlinear DGP model (nlDGP) , linear DGP (lDGP), and GR perturbations with the same expansion history (GRH) at z = 1. The left panels show the power spectra, and the right panels shows ratios to better see the differences. Two sets of computational boxes are shown for each case, covering a different range in k (see text). The solid line denotes the predictions from paper I for PnlDGP (left panel) and PGRH /PnlDGP (right panel).Tuesday, January 24, 2012
  22. 22. The key is to recognize that there are regions in the universe where the scalar ϕ is in the linear regime - in and around voids (see sim. by Chan Scoccimarro). Rewriting the scalar e.o.m.: −2 2 −2 2 2 ρm H ∂ ϕ + (H ∂ ϕ) ∼ α ρm ¯ in regions of sufficiently low density, the linear term dominates over the nonlinear term i.e. ϕ is unsuppressed by interactions. Consider a galaxy in such a region: the linear ϕext galaxy falls The galaxy (with its stars and dark matter) would fall under this external scalar field. The black hole won’t. Both of course still respond in the same way to the Einstein part of gravity.Tuesday, January 24, 2012
  23. 23. The key is to recognize that there are regions in the universe where the scalar ϕ is in the linear regime - in and around voids (see sim. by Chan Scoccimarro). Rewriting the scalar e.o.m.: −2 2 −2 2 2 ρm H ∂ ϕ + (H ∂ ϕ) ∼ α ρm ¯ in regions of sufficiently low density, the linear term dominates over the nonlinear term i.e. ϕ is unsuppressed by interactions. Consider a galaxy in such a region: the linear ϕext galaxy Central massive black hole becomes off-centered! falls The galaxy (with its stars and dark matter) would fall under this external scalar field. The black hole won’t. Both of course still respond in the same way to the Einstein part of gravity.Tuesday, January 24, 2012
  24. 24. The idea is to look for the offset of massive black holes from the centers of galaxies which are streaming out of voids. The offset should be correlated with the direction of the streaming motion. The massive black holes can take the form of quasars or low luminosity galactic nuclei i.e. Seyferts. The offset is estimated to be up to 0.1 kpc, for small galaxies.Tuesday, January 24, 2012
  25. 25. Topics for discussions: - Scalar-tensor theory as a framework for modifying gravity Weinberg’s theorem, quintessence - Conformal transformation: Einstein vs Jordan frame Einstein: extra (5th) force; Jordan: geodesic for test particle (only!) - Connection with self-acceleration Self-acceleration versus acceleration by dark energy - Large scale tests Growth rate, Psi versus Phi, photons - Small scale tests Screening mechanisms: chameleon versus Vainshtein Violations of the equivalence principle: chameleon - non-relativistic; Vainshtein - relativistic.Tuesday, January 24, 2012

×